SOLUTION: A car completes a journey in 10 minutes. For the first half of the distance the speed was 60km/hr and the second half the speed was 40 km/hr. How far is the journey?

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Question 970958: A car completes a journey in 10 minutes. For the first half of the distance the speed was 60km/hr and the second half the speed was 40 km/hr. How far is the journey?
Found 3 solutions by lwsshak3, ikleyn, greenestamps:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
A car completes a journey in 10 minutes. For the first half of the distance the speed was 60km/hr and the second half the speed was 40 km/hr. How far is the journey?
***
let x=total distance of journey
x/2=distance of first half of journey
x/2=distance of second half of journey
travel time=distance/speed
10 min=1/6 hr
..
60%2F%28x%2F2%29%2B40%2F%28x%2F2%29=1%2F6
120%2Fx%2B80%2Fx=1%2F6
lcd:x
120+80=x/6
x=1200
How far is the journey? 1200 km

Answer by ikleyn(53879) About Me  (Show Source):
You can put this solution on YOUR website!
.
A car completes a journey in 10 minutes. For the first half of the distance the speed was 60km/hr
and the second half the speed was 40 km/hr. How far is the journey?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~


        The solution in the post by @lwsshak3 is incorrect, and his answer is absurdist.
        It is because his setup equation is wrong.

        I came to bring a correct solution.


let x = total distance of journey
x/2 = distance of first half of journey
x/2 = distance of second half of journey
travel time = distance/speed
10 min = 1/6 hr

Write the time equation

        %28x%2F2%29%2F60 + %28x%2F2%29%2F40 = 1%2F6

        x%2F120 + x%2F80 = 1%2F6

Multiply both sides by 120*80.

        80x + 120x = 1600
        200x = 1600
        x = 1600/20 = 8

How far is the journey?     8 km         <<<---=== ANSWER

CHECK for the total time     %28%288%2F2%29%29%2F60 + %28%288%2F2%29%29%2F40 = 4%2F60 + 4%2F40 = 16%2F240 + 24%2F240 = 40%2F240 = 1%2F6 of an hour.     ! precisely correct !

Solved correctly.

It confirms that @lwsshak3 regularly uses his computer code and practically never checks
and even never looks/reads what the code really produces.



Answer by greenestamps(13355) About Me  (Show Source):
You can put this solution on YOUR website!


The other tutor provided a formal algebraic solution, using a standard method.

Here is a different, less formal solution.

Equal distances at different speeds in the ratio A:B means the times spent at the two speeds are in the ratio B:A.

In this problem, the two speeds are in the ratio 60:40 = 3:2, so the times spent at the two speeds are in the ratio 2:3.

The total time was 10 minutes; splitting that in the ratio 2:3 means the trip was 4 minutes (1/15 hour) at 60 km/h and 6 minutes (1/10 hour) at 40km/h.

Distance is rate times time, so the distance traveled at 60 km/h was %281%2F15%29%286%29=4 km and the distance traveled at 40 km/h was %281%2F10%29%2840%29=4 km.

So the total distance was 4+4 = 8 km.

ANSWER: 8 km